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# Pharmacokinetics: Lecture two

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IV Bolus One Compartment First Order Model

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### Pharmacokinetics: Lecture two

1. 1. Intravenous Bolus Administration Anas Bahnassi PhD RPhOne compartment Model
2. 2. LECTURE’S OBJECTIVESUpon the completion of this lecture the student should be able to:• Describe the different pharmacokinetic parameters.• Determine pharmacokinetic parameters from either plasma or urinary data.• State the equation for plasma drug concentration as a function of time.• Calculate the corresponding plasma drug concentration at time t• Calculate the intravenous bolus dose of a drug that will result in a target (desired) plasma drug concentration at time t. Anas Bahnassi PhD 2011 2
3. 3. XAssumptions • One-compartment model. Xu • First-order process. • Passive diffusion. • No metabolism takes place (elimination is 100% via renal excretion) • The drug is being monitored in blood (plasma/serum) and urine. 3 Anas Bahnassi PhD 2011
4. 4. Anas Bahnassi PhD 2011 4
5. 5. IV Bolus Equations:Anas Bahnassi PhD 2011 5
6. 6. Pharmacokinetic Parameters• Apparent volume of distribution (Vd).• Elimination half-life (t1/2).• Elimination rate constant (K0 or Kel).• Systemic clearance (Cls). Anas Bahnassi PhD 2011 6
7. 7. Apparent volume of distribution (Vd)• Concentrations are usually measured not masses.• Vd is a proportionality constant whose sole purpose is to relate the plasma concentration (Cp) and the mass of drug (X) in the body at a time.• It is not a physical volume. Anas Bahnassi PhD 2011 7
8. 8. Vd ConceptDrug Concentration in Beaker Drug Concentration in Beaker with charcoal Dose = 10mg Dose = 10mg Cp0 = 20mg/L Cp0 = 2mg/L Vd= 500mL Vd= 5000mL The concentration of KI is different although the volume of water in both beakers is the same. Anas Bahnassi PhD 2011 8
9. 9. Calculating Vd ������ Apparent volumes ������ = of distribution are ������������ given in units of volume (e.g. mL) or units of volume on a body weight basis (Lkg-1 body weight).Anas Bahnassi PhD 2011 9
10. 10. Elimination Half life (t1/2) The time (h, min, day, etc.) at which the mass (or Semi-logarithmic Paper amount) of unchanged drug becomes half (or 50%) of the initial mass of drug. Basic Pharmacokinetics: S. Jambhekar , Phillip Breen 2009 10Anas Bahnassi PhD 2011
11. 11. Elimination Half life (t1/2)When Cp = 0.5 (Cp)0 t = t1/2 Anas Bahnassi PhD 2011 11
12. 12. Elimination Rate Constant (k)Unit of k in first order process is reciprocal of time (h-1) ������ = ������������ + ������������ Elimination Rate Constant Metabolism Rate Excretion Constant Rate Constant Anas Bahnassi PhD 2011 12
13. 13. Elimination Rate Constant (k) X0= 0.963������ = = 0.173ℎ������ −1 250mg 4 125 %������������������������������������������������ = ������100 = 50% 250 M1= 75 75mg%������������������������������������������������������������������ = ������100 = 30% 250 50%������������������������������������������������������������������ = ������100 = 20% 250 M2= 50mg ������������ = ������������%������������. ������������������ = ������. ������������������������������������−������������������������ = ������������%������������. ������������������ = ������. ������������������������������−������������������������ = ������������%������������. ������������������ = ������. ������������������������������������−������ Xu= 125mg Anas Bahnassi PhD 2011 13
14. 14. Drawing a best-fit line through the Data Anas Bahnassi PhD 2011 14
15. 15. 40 X = 61.827e-0.526t353025201510 RL paper5 150 0 1 2 3 4 5 6 7 8 9 10 Anas Bahnassi PhD 2011
16. 16. Calculating PK Parameters From the SL graph ������0 t½= 1.3h ������������ = ������������0 Cp0= 63mg/mL. 600000 ������������ = = 9523.8������������ 63 = 9.5238������ ������. ������������������ ������ = ������. ������ Basic Pharmacokinetics: S. Jambhekar , Phillip Breen 2009 16 Anas Bahnassi PhD 2011
17. 17. Use of Urinary DataAmount remained to be excreted Rate of Excretion1. Urine collection is a non-invasive technique.2. More convenient sample collection3. Sample size is not restricting.4. The sampling time reflects cumulative drug concentration in urine collected over a period of time, rather than a drug concentration at a discrete time.5. Urinary data allows direct measurement of bioavailability, both absolute and relative, without the need of fitting the data to a mathematical model. 17 Anas Bahnassi PhD 2011
18. 18. Use of Urinary Data X Cumulative amount ������������������ Xu = ������������ ������ In Urine at time (t) ������������ ������������ ������ = ������0 (1 − ������ −������������������ ) Administered dose of drug Excretion Rate������������ ������ = ∞ Constant ������������ = ������0 Anas Bahnassi PhD 2011 18
19. 19. Amount Remaining To be excreted������������ ∞ − ������������ ������ = ������������������������������������ ������������������������������������������������������ ������������ ������������ ������������������������������������������������ = ������������������������������������ ������������ ������ℎ������ ������������������������ = ������������ Drug Totally Drug Totally Removed Unchanged Removed Unchanged Can not calculate Volume of Distribution 19 Anas Bahnassi PhD 2011
20. 20. Limitations1. Keep obtaining urine samples until noadditional drug practically appears in the urine,(t = 7 t½)2. Urine samples can not be lost, or urine fromany samples used in the determination of Xu(the exact volume of urine at each time intervalmust be known)3. A time-consuming method for a drug with along elimination half life.4. There is a cumulative build up of error. Anas Bahnassi PhD 2011 20
21. 21. Dose = 80mg The plot represents the cumulative quantity Anas Bahnassi PhD 2011 of the medication from the collected urine Drug TotallyRemoved Unchanged samples vs. the time. 21 Basic Pharmacokinetics: S. Jambhekar , Phillip Breen 2009
22. 22. The plot represents the amount remaining to be excreted of the medication vs. time Drug Totally Removed Unchanged������ = ������������ Can not calculate Anas Bahnassi PhD 2011 Volume of Distribution 22
23. 23. Rate of Excretion Method ������������������ = ������������ ������ ������������������ ������������ = ������������ ������������ ������−������������������ ������������ ������ = ������������ ������−������������������ average time between urine collectionaverage rateof excretion Anas Bahnassi PhD 2011 23
24. 24. The plot represents average rate ofexcretion within the time interval between samples collection vs. average time between urine samples collection Anas Bahnassi PhD 2011 24
25. 25. 25Anas Bahnassi PhD 2011
26. 26. 0.693 0.693������ = ������������ = = = 0.693ℎ������ −1 Anas Bahnassi PhD 2011 ������½ 1 26
27. 27. Questions:What is the concentration of drug 0, 2 and 4 hours after a dose of 500mg. Known pharmacokinetic parameters are apparent volume ofdistribution, Vd is 30 liter and the elimination rate constant, kel is 0.2hr-1 ?From the plot seen calculate allpharmacokinetic parameters thatyou can calculate Anas Bahnassi PhD 2011 27
28. 28. PharmacokineticsAnas Bahnassi PhD RPh abahnassi@gmail.com http://www.linkedin.com/in/abahnassi http://www.slideshare.net/abahnassi http://bahnassi.coursesites.com attribution – non-commercial – share alike